Jungle Outpost HDU - 3761 （半平面交）

  1 #include <bits/stdc++.h>
  2 using namespace std;
  3 const int maxn = 50010;
  4 const int inf = 0x3f3f3f3f;
  5 const double eps = 1e-8;
  6 struct Point {
  7     double x,y;
  8     Point (double x = 0, double y = 0) : x(x), y(y) {}
  9 };
 10 typedef Point Vector;
 11 Vector operator + (Vector a, Vector b) {
 12     return Vector (a.x + b.x, a.y + b.y);
 13 }
 14 Vector operator * (Vector a, double s) {
 15     return Vector (a.x * s, a.y * s);
 16 }
 17 Vector operator / (Vector a, double p) {
 18     return Vector (a.x / p, a.y / p);
 19 }
 20 Vector operator - (Point a, Point b) {
 21     return Vector (a.x - b.x, a.y - b.y);
 22 }
 23 bool operator < (Point a, Point b) {
 24     return a.x < b.x || (a.x == b.x && a.y < b.y);
 25 }
 26 int dcmp (double x) {
 27     if(fabs(x) < eps) return 0;
 28     return x < 0 ? -1 : 1;
 29 }
 30 bool operator == (const Point &a, const Point &b) {
 31     return dcmp(a.x - b.x) == 0 && dcmp(a.y - b.y) == 0;
 32 }
 33 double Dot(Vector a, Vector b) {
 34     return a.x * b.x + a.y * b.y;
 35 }
 36 double Cross (Vector a, Vector b) {
 37     return a.x * b.y - a.y * b.x;
 38 }
 39 //半平面交
 40 struct Line{
 41     Point p;
 42     Vector v;
 43     double rad;
 44     Line () {}
 45     Line (Point p, Vector v) : p(p), v(v) {
 46         rad = atan2(v.y,v.x);
 47     }
 48     bool operator < (const Line &L) const {
 49         return rad < L.rad;
 50     }
 51 };
 52 bool OnLeft(Line L, Point p) {
 53     return Cross(L.v, p - L.p) > 0;
 54 }
 55 Point GetLineIntersection (Line a, Line b) {
 56     Vector u = a.p - b.p;
 57     double t = Cross(b.v, u) / Cross(a.v, b.v);
 58     return a.p + a.v*t;
 59 }
 60 int HalfplaneIntersection(Line *L, int n) {
 61     sort(L, L+n);
 62     int first, last;
 63     Point *p = new Point[n];
 64     Line *q = new Line[n];  //双端队列
 65     q[first = last = 0] = L[0];
 66     for(int i = 1; i < n; i++) {
 67         while(first < last && !OnLeft(L[i], p[last-1])) last--;   //去尾
 68         while(first < last && !OnLeft(L[i], p[first])) first++; 
 69         q[++last] = L[i];
 70         if(dcmp(Cross(q[last].v, q[last-1].v)) == 0) {
 71             last--;
 72             if(OnLeft(q[last], L[i].p)) q[last] = L[i];
 73         }
 74         if(first < last) p[last-1] = GetLineIntersection (q[last-1],q[last]);
 75     }
 76     while(first < last && !OnLeft(q[first], p[last-1])) last--;  //删除无用平面
 77     delete []p;
 78     delete []q;
 79     if(last - first <= 1) return 0;  //空集
 80     return 1;
 81 }
 82 Point pp[maxn];
 83 Line line[maxn];
 84 int n;
 85 bool ck(int m){
 86     int cnt = 0;
 87     for(int i = 0; i < n; i++){
 88         line[cnt++] = Line(pp[i], pp[(i+m+1)%n] - pp[i]);
 89     }
 90     int ans = HalfplaneIntersection(line, cnt);
 91     return ans==0;
 92 }
 93 int main(){
 94     int t;
 95     //freopen("in.txt", "r", stdin);
 96     scanf("%d", &t);
 97     while(t--){
 98         scanf("%d", &n);
 99         for(int i = n-1; i >= 0; i--){
100             scanf("%lf %lf", &pp[i].x, &pp[i].y);
101         }
102         int L = 1, R = n-3;
103         while(L <= R) {
104             int m = (L+R)/2;
105             if(ck(m)) R = m-1;
106             else L = m+1;
107         }
108         printf("%d\n", L);
109     }
110 }